I have looked at the 1861 census for John Jeffries, and the way it is displayed in Ancestry, Eliza Parker is not part of the family.
I will agree with Kay99 as a monthly nurse, but John has an occupation of lamplighter, so whether he could afford a nurse could be problematic.
When checking Eliza Parker in the 1861 census, she shows up on her own, at the same address, with a gender of female!, and a relationship of wife. BUT, the way the relationship is written, it could be that of W for widow.
AC